Solve 3/4+(1/2-2/5):3/10+frac{1}{6}

$$\frac { 3 } { 4 } + ( \frac { 1 } { 2 } - \frac { 2 } { 5 } ) : \frac { 3 } { 10 } + \frac { 1 } { 6 }$$

Evaluate

$$\frac{5}{4}=1.25$$

Solution Steps

Least common multiple of 2 and 5 is 10. Convert \frac{1}{2} and \frac{2}{5} to fractions with denominator 10.

$$\frac{3}{4}+\frac{\frac{5}{10}-\frac{4}{10}}{\frac{3}{10}}+\frac{1}{6}$$

Since \frac{5}{10} and \frac{4}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{4}+\frac{\frac{5-4}{10}}{\frac{3}{10}}+\frac{1}{6}$$

Subtract 4 from 5 to get 1.

$$\frac{3}{4}+\frac{\frac{1}{10}}{\frac{3}{10}}+\frac{1}{6}$$

Divide \frac{1}{10} by \frac{3}{10} by multiplying \frac{1}{10} by the reciprocal of \frac{3}{10}.

$$\frac{3}{4}+\frac{1}{10}\times \frac{10}{3}+\frac{1}{6}$$

Multiply \frac{1}{10} times \frac{10}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{4}+\frac{1\times 10}{10\times 3}+\frac{1}{6}$$

Cancel out 10 in both numerator and denominator.

$$\frac{3}{4}+\frac{1}{3}+\frac{1}{6}$$

Least common multiple of 4 and 3 is 12. Convert \frac{3}{4} and \frac{1}{3} to fractions with denominator 12.

$$\frac{9}{12}+\frac{4}{12}+\frac{1}{6}$$

Since \frac{9}{12} and \frac{4}{12} have the same denominator, add them by adding their numerators.

$$\frac{9+4}{12}+\frac{1}{6}$$

Add 9 and 4 to get 13.

$$\frac{13}{12}+\frac{1}{6}$$

Least common multiple of 12 and 6 is 12. Convert \frac{13}{12} and \frac{1}{6} to fractions with denominator 12.

$$\frac{13}{12}+\frac{2}{12}$$

Since \frac{13}{12} and \frac{2}{12} have the same denominator, add them by adding their numerators.

$$\frac{13+2}{12}$$

Add 13 and 2 to get 15.

$$\frac{15}{12}$$

Reduce the fraction \frac{15}{12} to lowest terms by extracting and canceling out 3.

$$\frac{5}{4}$$

Factor

$$\frac{5}{2 ^ {2}} = 1\frac{1}{4} = 1.25$$